Question

what is the value of x + y?
a. 75°
b. 150°
c. 180°
d. 210°

Explanation:

Step1: Identify angle - relationship

Since the two lines \(m\) and \(n\) are parallel, \(y\) and the \(105^{\circ}\) angle are corresponding angles, so \(y = 105^{\circ}\).

Step2: Identify another angle - relationship

\(x\) and the \(105^{\circ}\) angle are supplementary angles (linear - pair). So \(x+105^{\circ}=180^{\circ}\), then \(x = 180^{\circ}-105^{\circ}=75^{\circ}\).

Step3: Calculate \(x + y\)

Substitute the values of \(x\) and \(y\) into \(x + y\). \(x + y=75^{\circ}+105^{\circ}=180^{\circ}\).

Answer:

C. \(180^{\circ}\)